The purpose of this research study is to determine the effects of gemcitabine and paclitaxel when given in combination for the treatment of non-small cell lung cancer. Specifically, this study will determine the extent to which these two drugs can prolong life, as well as the effects of these two drugs on your general well being and quality of life. The ability of the gemcitabine and paclitaxel combination to reduce tumor size and tumor related symptoms will also be determined. The type and severity of side effects that occur when these drugs are administered together will also be evaluated. Another goal of this study is to determine how well gemcitabine is eliminated or removed from the body, and whether this is affected by giving gemcitabine along with paclitaxel. The ability of a certain dose of gemcitabine to achieve certain concentrations in the blood will also be evaluated.